3c(c-2)=2c+6

Solution for 3c(c-2)=2c+6 equation:

Simplifying
3c(c + -2) = 2c + 6

Reorder the terms:
3c(-2 + c) = 2c + 6
(-2 * 3c + c * 3c) = 2c + 6
(-6c + 3c2) = 2c + 6

Reorder the terms:
-6c + 3c2 = 6 + 2c

Solving
-6c + 3c2 = 6 + 2c

Solving for variable 'c'.

Reorder the terms:
-6 + -6c + -2c + 3c2 = 6 + 2c + -6 + -2c

Combine like terms: -6c + -2c = -8c
-6 + -8c + 3c2 = 6 + 2c + -6 + -2c

Reorder the terms:
-6 + -8c + 3c2 = 6 + -6 + 2c + -2c

Combine like terms: 6 + -6 = 0
-6 + -8c + 3c2 = 0 + 2c + -2c
-6 + -8c + 3c2 = 2c + -2c

Combine like terms: 2c + -2c = 0
-6 + -8c + 3c2 = 0

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
-2 + -2.666666667c + c2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -2.666666667c + 2 + c2 = 0 + 2

Reorder the terms:
-2 + 2 + -2.666666667c + c2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -2.666666667c + c2 = 0 + 2
-2.666666667c + c2 = 0 + 2

Combine like terms: 0 + 2 = 2
-2.666666667c + c2 = 2

The c term is -2.666666667c.  Take half its coefficient (-1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
-2.666666667c + 1.777777780 + c2 = 2 + 1.777777780

Reorder the terms:
1.777777780 + -2.666666667c + c2 = 2 + 1.777777780

Combine like terms: 2 + 1.777777780 = 3.77777778
1.777777780 + -2.666666667c + c2 = 3.77777778

Factor a perfect square on the left side:
(c + -1.333333334)(c + -1.333333334) = 3.77777778

Calculate the square root of the right side: 1.943650632

Break this problem into two subproblems by setting 
(c + -1.333333334) equal to 1.943650632 and -1.943650632.

Subproblem 1
c + -1.333333334 = 1.943650632

Simplifying
c + -1.333333334 = 1.943650632

Reorder the terms:
-1.333333334 + c = 1.943650632

Solving
-1.333333334 + c = 1.943650632

Solving for variable 'c'.

Move all terms containing c to the left, all other terms to the right.

Add '1.333333334' to each side of the equation.
-1.333333334 + 1.333333334 + c = 1.943650632 + 1.333333334

Combine like terms: -1.333333334 + 1.333333334 = 0.000000000
0.000000000 + c = 1.943650632 + 1.333333334
c = 1.943650632 + 1.333333334

Combine like terms: 1.943650632 + 1.333333334 = 3.276983966
c = 3.276983966

Simplifying
c = 3.276983966

Subproblem 2
c + -1.333333334 = -1.943650632

Simplifying
c + -1.333333334 = -1.943650632

Reorder the terms:
-1.333333334 + c = -1.943650632

Solving
-1.333333334 + c = -1.943650632

Solving for variable 'c'.

Move all terms containing c to the left, all other terms to the right.

Add '1.333333334' to each side of the equation.
-1.333333334 + 1.333333334 + c = -1.943650632 + 1.333333334

Combine like terms: -1.333333334 + 1.333333334 = 0.000000000
0.000000000 + c = -1.943650632 + 1.333333334
c = -1.943650632 + 1.333333334

Combine like terms: -1.943650632 + 1.333333334 = -0.610317298
c = -0.610317298

Simplifying
c = -0.610317298

Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {3.276983966, -0.610317298}